Gore compiled 107 yards on 19 carries, becoming the first player in San Francisco franchise history to record five consecutive 100-yard rushing performances.
The Redskins, meanwhile, dropped their fourth straight and fell to 3-5.
John Beck went 30-of-47 through the air for 254 yards, a touchdown and an interception, while Roy Helu made 14 grabs for 105 yards and added 41 rushing yards on 10 carries in the loss.
Teacher apologizes for showing sexual image of herself in class
Scarlett Johansson steps out with fiance after pregnancy reveal